Beam-target double-spin asymmetry in quasielastic electron scattering off the deuteron with CLAS

Background: The deuteron plays a pivotal role in nuclear and hadronic physics, as both the simplest bound multinucleon system and as an effective neutron target. Quasielastic electron scattering on the deuteron is a benchmark reaction to test our understanding of deuteron structure and the properties and interactions of the two nucleons bound in the deuteron.

Purpose: The experimental data presented here can be used to test state-of-the-art models of the deuteron and the two-nucleon interaction in the final state after two-body breakup of the deuteron. Focusing on polarization degrees of freedom, we gain information on spin-momentum correlations in the deuteron ground state (due to the $D$-state admixture) and on the limits of the impulse approximation (IA) picture as it applies to measurements of spin-dependent observables like spin structure functions for bound nucleons. Information on this reaction can also be used to reduce systematic uncertainties on the determination of neutron form factors or deuteron polarization through quasielastic polarized electron scattering.

Method: We measured the beam-target double-spin asymmetry ($A_{\left|\right|}$) for quasielastic electron scattering off the deuteron at several beam energies ($1.6\text{–}1.7$, 2.5, 4.2, and $5.6\text{–}5.8\mathrm{GeV}$), using the CEBAF Large Acceptance Spectrometer (CLAS) at the Thomas Jefferson National Accelerator Facility. The deuterons were polarized along (or opposite to) the beam direction. The double-spin asymmetries were measured as a function of photon virtuality $Q^2(0.13\text{–}3.17{(\mathrm{GeV}/c)}^2)$, missing momentum $\left(p_m=0.0\text{–}0.5\mathrm{GeV}/c\right)$, and the angle between the (inferred) spectator neutron and the momentum transfer direction $\left({\theta }_{nq}\right)$.

Results: The results are compared with a recent model that includes final-state interactions (FSI) using a complete parametrization of nucleon-nucleon scattering, as well as a simplified model using the plane wave impulse approximation (PWIA). We find overall good agreement with both the PWIA and FSI expectations at low to medium missing momenta $\left(p_m\le 0.25\mathrm{GeV}/c\right)$, including the change of the asymmetry due to the contribution of the deuteron $D$ state at higher momenta. At the highest missing momenta, our data clearly agree better with the calculations including FSI.

Conclusions: Final-state interactions seem to play a lesser role for polarization observables in deuteron two-body electrodisintegration than for absolute cross sections. Our data, while limited in statistical power, indicate that PWIA models work reasonably well to understand the asymmetries at lower missing momenta. In turn, this information can be used to extract the product of beam and target polarization $\left(P_b{P}_t\right)$ from quasielastic electron-deuteron scattering, which is useful for measurements of spin observables in electron-neutron inelastic scattering. However, at the highest missing (neutron) momenta, FSI effects become important and must be accounted for.

Figure 1

Results for the tensor analyzing power $A_d^T$ in ${}^2\mathrm{H}(e,e^{\prime }p)n$ from NIKHEF, plotted vs missing momentum $p_m$ (a) and vs the cosine of the opening angle $\theta$ between the momentum transfer vector $\vec{q}$ and the momentum in the center-of-mass system (b). Theoretical curves from Arenhövel are also shown. Short-dashed curves are results for plane-wave Born approximation (PWBA), long-dashed curves include FSIs, and solid curves represent the full calculation [38].

Figure 2

NIKHEF results for the vector analyzing power $A_{ed}^V$ as a function of missing momentum at $Q^2=0.21$ (GeV/${c)}^2$ [25]. The curves are again from Arenhövel et al. [9, 39].

Figure 3

Results from BLAST for ${\mathrm{A}}_d^T$ [panels (a) and (b)] and ${\mathrm{A}}_{ed}^V$ [panels (c) and (d)] for $0.2<Q^2<0.3{(\mathrm{GeV}/\mathrm{c})}^2$, for both parallel [panels (a) and (c)] and perpendicular [panels (b) and (d)] kinematics. Theoretical curves have been calculated including meson exchange currents (MEC), isobar currents (IC), and relativistic correction (RC) [40].

Figure 4

Double-spin asymmetry $A_{ed}^V$ as measured in Hall C, vs scattered electron energy ($E^{\prime }$) and vs the angle between the neutron and the $\vec{q}$ vector. The theoretical curves are predicted asymmetries using different scaled values of $G_E^n$ [42].

Figure 5

A cross section view of the CLAS detector.

Figure 6

A plot of missing energy vs missing momentum where the red lines represent the cuts placed on the data.

Figure 7

Distribution of events in missing mass [Eq. (12)] for two different kinematic bins (left: $E_{\mathrm{Beam}}=1.6$ GeV, $Q^2$ bin 1, $p_m$ bin 1, $cos{\theta }_{nq}$ bin 1; right: $E_{\mathrm{Beam}}=1.6$ GeV, $Q^2$ bin 1, $p_m$ bin 1, $cos{\theta }_{nq}$ bin 2). The inelastic background was fitted by a Gaussian tail shown as the solid and dotted green lines (the dotted line is the interpolation between the two fit regions). The bottom panel (b) is an example for a kinematic setting where, due to CLAS acceptance, no peak is seen within the missing mass cut Eq. (13), indicated by vertical dotted red lines. Bins such as these were discarded in the further analysis.

Figure 8

Same as Fig. 7 for two additional kinematic bins (left: $E_{\mathrm{Beam}}=4.2$ GeV, $Q^2$ bin 1, $p_m$ bin 3, $cos{\theta }_{nq}$ bin 0; right: $E_{\mathrm{Beam}}=5.7$ GeV, $Q^2$ bin 3, $p_m$ bin 4, $cos{\theta }_{nq}$ bin 1).

Figure 9

Distribution of counts vs $\mathrm{\Delta }{p}_{\theta }$ for ${\mathrm{ND}}_3$ targets. The ${}^1\mathrm{H}$ peak (green) can be seen on top of the ${}^2\mathrm{H}$ peak (blue) with the scaled background (red).

Figure 10

Count rate differences for antiparallel vs parallel beam and target polarization for the ${\mathrm{ND}}_3$ target, vs $\mathrm{\Delta }{\mathrm{p}}_{\theta }$. The distribution is fit with a free scale parameter for both D and H. The lowest ${\chi }^2$ results from a fit with no contribution from free protons.

Figure 11

$A_{\left|\right|}$ for beam energies of 1.6–1.7 GeV and $Q^2$ bin 1 ($0.38{\mathrm{GeV}}^2/c^2\le Q^2\le 0.77{\mathrm{GeV}}^2/c^2$; average $\overline{Q^2}=0.56{\mathrm{GeV}}^2/c^2$), vs the cosine of the angle ${\theta }_{nq}$ between the direction of the virtual photon and the spectator neutron in the reaction ${}^2\vec{\mathrm{H}}(\vec{e},e^{\prime }p)n$. The different symbols refer to different bins in missing momentum: red circles are for $p_m\le 0.05\mathrm{GeV}/c$, blue squares for $0.05\mathrm{GeV}/c\le p_m\le 0.15\mathrm{GeV}/c$, purple triangles for $0.15\mathrm{GeV}/c\le p_m\le 0.25\mathrm{GeV}/c$, orange inverted triangles for $0.25\mathrm{GeV}/c\le p_m\le 0.35\mathrm{GeV}/c$, and green star symbols for $0.35\mathrm{GeV}/c\le p_m\le 0.5\mathrm{GeV}/c$. The inner error bars with horizontal risers indicate the statistical uncertainties, while the full error bars correspond to the statistical and systematic uncertainties added in quadrature. The dashed lines correspond to a PWIA prediction and the solid lines to a prediction including FSI, as explained in the text. They are color coded for the same missing momentum bins as the data.

Figure 12

$A_{\left|\right|}$ for a beam energy of 2.5 GeV and the same $Q^2$ bin as before (average $\overline{Q^2}=0.54{\mathrm{GeV}}^2/c^2$). All symbols and colors have the same meaning as in Fig. 11.